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Math Expert V
Joined: 02 Sep 2009
Posts: 58315

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1
3 00:00

Difficulty:   25% (medium)

Question Stats: 82% (01:57) correct 18% (02:23) wrong based on 191 sessions

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If a car had traveled 20 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 km, at what speed did it travel?

A. 35 kmh
B. 40 kmh
C. 50 kmh
D. 60 kmh
E. 65 kmh

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Math Expert V
Joined: 02 Sep 2009
Posts: 58315

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Official Solution:

If a car had traveled 20 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 km, at what speed did it travel?

A. 35 kmh
B. 40 kmh
C. 50 kmh
D. 60 kmh
E. 65 kmh

Solve the equation $$\frac{60}{x} = \frac{60}{x + 20} + 0.5$$. Backsolve: $$\frac{60}{40} = \frac{60}{40 + 20} + 0.5$$.

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Intern  B
Joined: 17 May 2016
Posts: 27
GMAT 1: 740 Q46 V46 Show Tags

Hi,

Is it possible to calculate it algebraically ?

I get stuck with two unknown, even if I know that is quicker to back solve, I do not understand why it is not solvable ?

Many thanks in advance for your kind help
Math Expert V
Joined: 02 Sep 2009
Posts: 58315

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nickimonckom wrote:
Hi,

Is it possible to calculate it algebraically ?

I get stuck with two unknown, even if I know that is quicker to back solve, I do not understand why it is not solvable ?

Many thanks in advance for your kind help

Which two unknowns are you talking about? There is only one unknown in the equation above. If you simplify $$\frac{60}{x} = \frac{60}{x + 20} + 0.5$$ you'll get quadratic equation which will give two values of x: -60 (discard) and 40.
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Intern  B
Joined: 17 May 2016
Posts: 27
GMAT 1: 740 Q46 V46 Show Tags

I mean that if I set up the table, I get the following :

FIRST MOVE : $$r*(t+\frac{1}{2}) = 60$$
2ND MOVE : $$(r+20)*t = 60$$

Then, since they are equal :
$$r*(t+\frac{1}{2}) = (r+20)*t$$
$$rt + \frac{r}{2} = rt + 20t$$
$$r = 40t$$

Then I have a problem with the unit, I know that 40 is the good value but I am not supposed to express a rate and a time, only a rate.

Manager  S
Joined: 23 Jan 2016
Posts: 180
Location: India
GPA: 3.2

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Could you please share some links to questions similar to this? Thank you.
Math Expert V
Joined: 02 Sep 2009
Posts: 58315

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OreoShake wrote:
Could you please share some links to questions similar to this? Thank you.

Check Distance/Rate problems from our Questions' Bank: https://gmatclub.com/forum/viewforumtags.php

Hope it helps.
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Current Student B
Joined: 28 Dec 2016
Posts: 88
Location: United States (IL)
Concentration: Marketing, General Management
Schools: Johnson '20 (M)
GMAT 1: 700 Q47 V38 Show Tags

For those of you wanting to set up an equation and solve it w/o plugging in, I can chime in to help.
Since traveling at 20kmh faster saves 1/2 hour, we can say that:
60/R - 60/(R+20) = 1/2, which is basically saying:
(Time at Reg Speed) - (Time +20kmh faster) = (30 mins)

Solving, we get:
(R+60)(R-40)=0
R= -60, 40

Rate can not be negative, therefore, 40 is the winner.
Manager  S
Joined: 26 Sep 2018
Posts: 56
Location: Sweden

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I used the options.

60/40= 1.5 60/60=1

B is the only one that fits. Re: M23-20   [#permalink] 14 Jan 2019, 12:23
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